Source: cirosantilli/decidability-of-hilbert-s-tenth-problem-in-modular-arithmetic
= Decidability of Hilbert's tenth problem in modular arithmetic
https://www.jstor.org/stable/1970438 says for <prime> modulo there is an algorithm.
Question for non-prime modulo: https://math.stackexchange.com/questions/4944623/are-diophantine-equations-decidable-in-modular-arithmetic